By the formula for electric potential $V=\frac{kq}{r}$ it is apparent that potential depends solely on the source charge and distance of a point from it and has nothing to with resistance. So when we move along a wire(even superconducting) shouldn't the value of electric potential change as the distance from source charge (battery) is changing? According to what I have studied potential drops across a resistance due to collisions caused as a result of less mobility of charges that sucks out energy from them into heat energy thereby decreasing the potential and this isn't the case in ideal wires so potential remains constant.And this completely makes sense. But at the end of the day potential still depends on the source charge and distance of a point from it we desire to calculate potential at. Possibly a dumb question but still it's bothering me so much, please help with the insights. Thank you
1 Answer
The electric potential is the amount of work required to move a unit charge from some reference point to a specific point against an electric field.
Since superconductors have zero resistance no work is required to move charge in them and thus the potential along them is constant. Since the electric field equals the gradient of the potential, it is zero along the superconductor.
If the superconductor were to be connected to a battery the current would be limited by the internal resistance of the battery. All the change in potential will occur in the internal resistance of the battery.
Ordinary conductors have resistance so work is required by an electric field to move charge through them, resulting in a change in potential along the conductor.
Hope this helps.
-
$\begingroup$ But in vaccum(which also has zero resistance) work has to be done to bring charges from a reference point (infinity by convention) to a given configuration. The formula for potential V=kq/r doesn't count resistance to be a factor affecting it $\endgroup$ Commented Jan 15, 2022 at 5:21
-
$\begingroup$ See this: physics.stackexchange.com/questions/178831/… $\endgroup$– Bob DCommented Jan 15, 2022 at 10:28
-
$\begingroup$ After seeing Derek's video on electricity it started making all the sense, the surface charges description of electricity mechanism made it all clear. Anyways thanks Bob. $\endgroup$ Commented Jun 5, 2022 at 3:10
-
$\begingroup$ Turns out that the macroscopic rules of potential drop are just conventions which mataches the results of microscopic level. $\endgroup$ Commented Jun 5, 2022 at 3:13